Name: Date: You must answer all questions. Please show works for all questions that need work. You can show the work in the space provided by each question. If you need more room you can do the work on loose leaf and attach it to this worksheet. This assignment will count as a quiz for the 1st. Quarter. It will be collected during the 1st week of classes. No late papers will be accepted. If you misplace it you can find a downloadable copy on www.mshillig.org. 1. Simplify: (4x 2 3x + 8) (3x 2 5) 1. (1) x 2 3x 3 (2) x 2 3x + 13 (3) 7x 2 3x 3 (4) 7x 2 3x + 13 2. Simplify: (3x 2 5x + 9) + (7x 2 + 8x 15) 2. (1) 10x 2 + 3x 6 (2) 10x 2 3x 6 (3) 10x 2 3x + 6 (4) 10x 2 13x 24 3. Simplify: 5x 2 4x + 7 (2x 2 3x 4) 3. (1) 3x 2 7x + 11 (2) 3x 2 x + 11 (3) 3x 2 x + 3 (4) 3x 2 x 3 4. Simplify: (2a 3 + 5 4a + 7a 2 ) (4a 2 6a + 3 + 3a 3 ) 4. (1) a 3 + 3a 2 + 2a + 2 (2) 5a 3 + 3a 2 10a + 2 (3) 5a 3 + 3a 2 10a + 8 (4) 5a 3 + 3a 2 + 2a + 2 page 1
5. The length of a side of a square is represented by 4x 1. Express the perimeter of the square in terms of x. 5. (1) 16x 4 (2) 4x 2 + 1 (3) 16x 1 (4) 4x 2 4x + 1 6. Simplify: 4x 3[5x 2(3 x) + 6x] 6. (1) 18 + 35x (2) 18 41x (3) 18 35x (4) 9 41x 7. Multiply: 2m 4 (5m 3 + 4m 1) 7. (1) 11m 8 (2) 10m 7 + 8m 5 2m 4 (3) 10m 12 + 8m 4 (4) 10m 7 + 8m 4 2 8. Simplify: (8x 1)(4x + 3) 8. (1) 12x 2 4x + 2 (2) 32x 2 + 20x 3 (3) 32x 2 4x 3 (4) 32x 2 + 24x 3 page 2
9. The lengths of consecutive sides of a rectangle are represented by 2x + 1 and 3x + 2. Express the area of the rectangle in terms of x. 9. (1) 6x 2 + 7x + 2 (2) 5x + 3 (3) 6x 2 + 2 (4) 6x + 3 10. Simplify: (3x 2) 2 10. (1) 6x 4 (2) 6x 2 + 4 (3) 9x 2 12x + 4 (4) 9x 2 6x + 4 11. Multiply: (2x 2 + 3x 4)(2x + 5) 11. (1) 4x 3 + 16x 2 + 7x 20 (2) 4x 3 + 16x 2 + 7x + 20 (3) 4x 3 + 16x 2 7x 20 (4) 4x 3 + 16x 2 23x 20 12. Multiply: (x 2 + 2x + 3)(x 2 2x 1) 12. (1) x 4 + 2x 2 3 (2) x 4 2x 2 8x 3 (3) 2x 2 4x 3 (4) 2x 2 + 2 13. Expand and simplify: (x 2y + 3z) 2 13. (1) x 2 + 4y 2 + 9z 2 + 4xy + 6xz 12yz (2) x 2 + y 2 + 9z 2 + 4xy + 6xz 12yz (3) x 2 + 4y 2 + 9z 2 4xy + 6xz 12yz (4) x 2 + 4y 2 + 6z 2 + 4xy + 6xz 12yz page 3
14. Simplify: (x 2 + y 2 )(x 3 5x 2 y + 3xy 2 y 3 ) 14. (1) x 5 5x 4 y + 4x 6 y 4 6x 4 y 6 + 3xy 4 y 5 (2) x 5 5x 4 y + 4x 3 y 2 6x 2 y 3 + 3xy 4 y 5 (3) x 6 5x 4 y + x 3 y 2 2x 2 y 2 x 2 y 3 + 3xy 4 y 6 (4) x 6 5x 8 y + x 6 y 4 2x 4 y 4 x 4 y 6 + 3xy 8 y 6 15. Solve the following system of equations for y: 15. 7x + 5y = 6 5x + 2y = 5 (1) 5 3 (2) 13 11 (3) 1 3 (4) 5 3 16. Solve the following system of equations for x: 16. 7x + 5y = 6 5x + 2y = 5 (1) 13 11 (2) 1 3 (3) 1 3 (4) 5 3 17. Find P( 1 2 ) given that P(x) = 2x3 5x 2 + 6x 5. 17. page 4
18. The vertical line test is a quick way to check if a graph is a function. If a vertical line can be drawn which touches the graph at more than one point, then the graph is not a function. Use the vertical line test to determine which of the following graphs represents a function. 18. I. II. III. IV. (1) I and II (2) II and III (3) II and IV (4) IV only 19. This equation represents what type of function? 19. y = x 4 + 2 (1) linear (2) quadratic (3) exponential (4) absolute value page 5
20. This equation represents what type of function? 20. y = 3x 2 5 (1) quadratic (2) exponential (3) absolute value (4) cubic 21. Which of the following is a quadratic function? 21. (1) f(x) = 3x 4 2x 2 + 7 (2) f(x) = 3x 5 (3) f(x) = 2x 2 3x + 6 (4) f(x) = 3 22. Which of the following statements is not true about the function y = 2x + 2? 22. (1) The graph of the function will intersect at 2 on the y-axis. (2) The graph of the function slopes down 2 units, and right 1 unit. (3) If the value of x is greater than 1, the value of y becomes negative. (4) If the value of x is positive, the value of y is also positive. 23. What is the domain of the given relation? 23. {( 1, 4), (4, 3), (4, 4), (1, 3)} (1) { 1, 3, 4} (2) {4, 3, 4} (3) {3, 1, 4} (4) { 1, 1, 4} page 6
24. Which of the following equations has a domain of all real numbers and a range where y 2? 24. (1) y = 4(x + 5) 2 2 (2) y = 4(x + 5) 2 + 2 (3) y = 4(x + 5) 2 2 (4) y = 4(x + 5) 2 + 2 25. What is the difference between the domain and range? 25. 26. How many solutions are shown by the graph of the quadratic function? 26. (1) zero (2) one (3) two (4) three page 7
27. How many solutions are shown by the graph of the quadratic function? 27. (1) zero (2) one (3) two (4) three 28. The table contains values for x and y in a quadratic function. 28. x y 3 12 2 0 1 8 0 12 1 12 2 8 3 0 What are the roots of the function? (1) 0 and 12 (2) 12, 2 and 3 (3) 12, 0 and 1 (4) 2 and 3 page 8
29. A microbiologist is studying a bacterial culture. Every hour she counts the number of bacteria. Her data is recorded in the table. What is the average increase between 10 am and 1 pm? Round to the nearest integer. 29. Time Number of bacteria 8 am 31 9 am 67 10 am 161 11 am 368 12 pm 842 1 pm 1918 2 pm 4433 3 pm 10172 (1) 639 bacteria per hour (2) 617 bacteria per hour (3) 586 bacteria per hour (4) 439 bacteria per hour 30. Which of the following represents the graph of f(t) = 2t 2 + 4t 3? 30. (1) (2) (3) (4) page 9
31. Which of the following is the graph of y = 2(x + 3) 2 1? 31. (1) (2) (3) (4) 32. Which of the following graphs represents the equation y = x 2 2x + 4? 32. (1) (2) (3) (4) page 10
33. Factor: 9x 2 16 33. (1) (3x + 4)(3x + 4) (2) (3x + 4)(3x 4) (3) (3x + 2)(3x + 8) (4) (3x 4)(3x 4) 34. Factor: 100 w 2 34. (1) (w + 10)(w 10) (2) 1(10 + w)(10 w) (3) (w + 10)(w + 10)( 1) (4) (10 w)(10 + w) 35. Factor: m 2 1 81 35. (1) (m 1 27 )(m + 1 3 ) (2) (m 1 9 )(m + 1 9 ) (3) (m 1 9 )2 (4) (m 1 9 )(m 1 9 ) 36. Factor completely: 18x 2 63x 36. (1) 3x(6x 21) (2) 9(2x 2 7x) (3) 9x(2x 8) (4) 9x(2x 7) page 11
37. Factor: x 2 + 7x + 12 37. (1) (x + 4)(x + 3) (2) (x + 12)(x + 1) (3) (x + 7)(x + 5) (4) (x 4)(x 3) 38. Factor: x 2 4x 12 38. (1) (x + 6)(x 2) (2) (x + 2)(x 6) (3) (x + 7)(x 3) (4) (x 4)(x + 3) 39. Factor: 2p 2 + p 6 39. (1) (2p 3)(p + 2) (2) (2p 5)(p 1) (3) (2p + 3)(p 2) (4) (2p 1)(p + 6) 40. Factor: 3q 2 + q 2 40. (1) (3q + 1)(q 1) (2) (3q + 2)(q 1) (3) (3q 2)(q + 1) (4) (3q 1)(q 1) page 12
41. Factor: 4x 2 x 3 41. (1) (2x 3)(2x + 1) (2) (2x + 3)(2x 1) (3) (4x 3)(x + 1) (4) (4x + 3)(x 1) 42. Factor: 2x 2 + 13x 15 42. (1) (2x + 15)(x 1) (2) (2x 5)(x + 3) (3) (2x + 5)(x 3) (4) (2x 1)(x 15) 43. Factor: 6a 2 5ab 4b 2 43. (1) (3a + 2)(2a 2) (2) (3a 4b)(2a + b) (3) (3a + 4b)(2a + b) (4) (3a 4b)(2a b) 44. Simplify: (a n+1 ) 5 44. (1) a n+5 (2) a n+6 (3) a 5n+1 (4) a 5n+5 page 13
45. Expand and simplify: (x 3n 5)(x 3n + 7) 45. (1) x 6n 2x 3n 35 (2) x 6n + 2x 3n 35 (3) x 9n2 2x 6n 35 (4) x 6n 2x 3n + 35 46. Simplify: ( 7x) 0 + (5x) 0 5x 0 46. (1) 5 (2) 4 (3) 3 (4) 3 47. Simplify: x 2 + x 3 47. (1) x 2 6 (2) 5 6x (3) 5x 6 (4) 6 5x 48. Simplify: 24b 3 8b 2 8b 2 48. (1) 3b 2 + 1 (2) 24b 2 + 1 (3) 3b + 1 (4) 24b + 1 49. Simplify: 50r 2 20r 10r 49. (1) 50r + 2 (2) 5r + 2 (3) 5r 2 (4) 5r 2 + 2 page 14
50. Simplify: 15m 9 n 10 45m 5 n 7 15m 3 n 5 50. (1) m 12 n 15 30m 8 n 12 (2) m 12 n 15 3m 8 n 12 (3) m 6 n 5 45m 2 n 2 (4) m 6 n 5 3m 2 n 2 page 15
Problem-Attic format version 4.4.266 c 2011 2015 EducAide Software Licensed for use by Denise Hillig Terms of Use at www.problem-attic.com 06/03/2016 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Objective: A.REI.6 16. Objective: A.REI.6 17. Answer: Objective: 3 F.IF.2 18. Objective: F.IF.1 19. Objective: F.IF.1 20. Objective: F.IF.1 21. Objective: F.IF.1 22. Objective: F.IF.1 23. Objective: F.IF.1 24. Objective: F.IF.1 25. Answer: Objective: 26. Objective: F.IF.4 27. Objective: F.IF.4 The domain is the set of first ordered pairs. The range is the set of second ordered pairs. F.IF.1
Teacher s Key Page 2 28. Objective: F.IF.4 29. Objective: F.IF.6 30. Objective: F.IF.7A 31. Objective: F.IF.7A 32. Objective: F.IF.7A 33. 34. 35. 43. 44. Objective: A.SSE.3C 45. Objective: A.SSE.3C 46. Objective: A.SSE.2 47. Objective: A.SSE.2 48. Objective: A.SSE.2 49. Objective: A.SSE.2 50. Objective: A.SSE.2 36. 37. 38. 39. 40. 41. 42.